Chapter 10 - Area - 10-4 Perimeters and Areas of Similar Figures - Practice and Problem-Solving Exercises - Page 639: 27

The ratio of the perimeters is equal to $2:3$ and the ratio of the areas is equal to the square of the scale factor $4:9$.

We are given the scale factor $2:3$ We know that the ratio of the perimeters of two smaller figures is the same as the ratio of the scale factor, and the ratio of their areas is the same as the square of the ratio of the scale factor. Now, the ratio of the perimeters of two smaller figures is equal to $2:3$. So, the ratio of the areas is equal to the square of the scale factor, which is $2^2:3^2=4:9$.